<documentation xmlns="http://cellml.org/tmp-documentation"> Model Status This version has had a stimulus protocol component added to allow the model to simulate multiple action potentials, has been unit checked and curated and is known to run in COR and PCEnv. <sect1 id="sec_structure"> Model Structure In a series of papers published in 1952, A.L. Hodgkin and A.F. Huxley presented the results of a series of experiments in which they investigated the flow of electric current through the surface membrane of the giant nerve fibre of a squid. In the summary paper of the Hodgkin and Huxley model, the authors developed a mathematical description of the behaviour of the membrane based upon these experiments, which accounts for the conduction and excitation of the fibre. The form of this description has been used as the basis for almost all other ionic current models of excitable tissues, including Purkinje fibres and cardiac atrial and ventricular muscle. The summary paper is cited below: A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve, A. L. Hodgkin and A. F. Huxley, 1952, The Journal of Physiology , 117, 500-544. PubMed ID: 12991237 <informalfigure float="0" id="fig_circuit_diagram"> <mediaobject> <imageobject> <objectinfo> Electrical circuit describing the current across the cell membrane </objectinfo> <imagedata fileref="hodgkin_1952.png" /> </imageobject> </mediaobject> A schematic cell diagram describing the current flows across the cell membrane that are captured in the Hodgkin Huxley model. </informalfigure> </sect1> </documentation>
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The stimulus amplitude (20 microamperes per cm2) and duration (0.5 ms) were taken from the single stimulus in the previous version. 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Version 05 was created by Penny Noble of Oxford University and is known to run in COR and PCEnv. The intial voltage membrane potential was changed from 0 mV to the correct value of -75 mV. 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</cmeta:modification> <dc:publisher xml:lang="en">The University of Auckland, Bioengineering Institute</dc:publisher> <created> <rdf:Description rdf:about="rdf:#665adec2-47bb-4f04-80a1-68f545e81a0e"> <W3CDTF xml:lang="en">2002-03-26T00:00:00+00:00</W3CDTF> </rdf:Description> </created> <cmeta:modification> <rdf:Description rdf:about="rdf:#11e3f403-75e7-4da6-9f6b-c5732c0cab1d"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#b7d9bdf8-8ab9-4b18-903c-84dc2b140727"> <vcard:N rdf:resource="rdf:#2513dee6-5449-443a-b035-2ff762ff3069"/> </rdf:Description> </cmeta:modifier> <modified> <rdf:Description rdf:about="rdf:#140c4615-dbeb-4856-aa9c-68f554470dfa"> <W3CDTF xml:lang="en">2007-06-20T16:01:50+12:00</W3CDTF> </rdf:Description> </modified> </rdf:Description> </cmeta:modification> <cmeta:modification> <rdf:Description rdf:about="rdf:#926f9f08-b397-491a-ac44-76e38b182232"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#d7dedc5f-038d-45c5-b191-69311c173c69"> <vcard:N> <rdf:Description 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Bioengineering Institute</vcard:Orgunit> </rdf:Description> </vcard:ORG> <vcard:EMAIL> <j.1:internet rdf:about="rdf:#18be6072-0bb2-486b-bf47-d786a8ccb00a"> <rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value> </j.1:internet> </vcard:EMAIL> <vcard:N> <rdf:Description rdf:about="rdf:#e64f82a7-a34d-4f8b-8e60-012dbf5ea240"> <vcard:Other xml:lang="en">May</vcard:Other> <vcard:Given xml:lang="en">Catherine</vcard:Given> <vcard:Family xml:lang="en">Lloyd</vcard:Family> </rdf:Description> </vcard:N> </rdf:Description> </dc:creator> <cmeta:modification> <rdf:Description rdf:about="rdf:#8fd18725-5764-4794-8857-23e4f6ce4b18"> <cmeta:modifier> <rdf:Description rdf:about="rdf:#18a9b9a3-ea24-4c7d-9df0-4f3663e434bd"> <vcard:N rdf:resource="rdf:#3b0e83c3-4898-4081-84fa-85c0d2807054"/> </rdf:Description> </cmeta:modifier> <modified> <rdf:Description rdf:about="rdf:#6875edb4-a9cd-4bb6-b8f9-03b2c7cc8124"> <W3CDTF xml:lang="en">2007-06-15T12:32:55+12:00</W3CDTF> </rdf:Description> </modified> </rdf:Description> </cmeta:modification> </rdf:Description> <rdf:Description rdf:about="http://www.cellml.org/cellml/1.0#hodgkin_huxley_squid_axon_1952"> <j.0:reference> <rdf:Description rdf:about="rdf:#c1c62bec-a4f9-4b41-91ab-bbc81d473192"> <dc:subject> <rdf:Description rdf:about="rdf:#34d6c118-3d31-4355-90dc-a2cb5ef18374"> <j.0:subject_type xml:lang="en">keyword</j.0:subject_type> <rdf:value> <rdf:Bag rdf:about="rdf:#e9e44e76-9801-4440-a074-6509ae83c1b7"> <rdf:li xml:lang="en">Neuron</rdf:li> <rdf:li xml:lang="en">giant axon</rdf:li> <rdf:li xml:lang="en">electrophysiology</rdf:li> </rdf:Bag> </rdf:value> </rdf:Description> </dc:subject> </rdf:Description> </j.0:reference> <j.0:reference> <rdf:Description rdf:about="rdf:#2f069a61-06ba-4782-a877-f31e770cdf0d"> <j.0:JournalArticle> <rdf:Description rdf:about="rdf:#6a5c1370-80c1-4b42-aead-44170b5e073e"> <j.0:Journal> <rdf:Description rdf:about="rdf:#eee0af8e-5256-4021-9426-80fe492518bc"> <dc:title xml:lang="en">Journal of Physiology</dc:title> </rdf:Description> </j.0:Journal> <j.0:first_page xml:lang="en">500</j.0:first_page> <issued> <rdf:Description rdf:about="rdf:#957446e8-2852-4457-a3f6-0e87906f21b9"> <W3CDTF xml:lang="en">1952-01-01</W3CDTF> </rdf:Description> </issued> <j.0:volume xml:lang="en">117</j.0:volume> <j.0:last_page xml:lang="en">544</j.0:last_page> <dc:title xml:lang="en">A quantitative description of membrane current and its application to conductance and excitation in nerve</dc:title> <dc:creator> <rdf:Seq rdf:about="rdf:#5aa345d1-498a-40fe-852c-be5a6c19cb10"> <rdf:li> <j.0:Person rdf:about="rdf:#51a60dc9-2f70-4eb6-845a-1dafe7feb919"> <vcard:N> <rdf:Description rdf:about="rdf:#9402b850-7050-4483-9cc7-a84fe2f91be2"> <vcard:Other xml:lang="en">L</vcard:Other> <vcard:Given xml:lang="en">A</vcard:Given> <vcard:Family xml:lang="en">Hodgkin</vcard:Family> </rdf:Description> </vcard:N> </j.0:Person> </rdf:li> <rdf:li> <j.0:Person rdf:about="rdf:#3e67593e-eafa-479e-8369-1879d475ea1a"> <vcard:N> <rdf:Description rdf:about="rdf:#0f72a1b1-ef97-4005-ad81-81353e3383ef"> <vcard:Other xml:lang="en">F</vcard:Other> <vcard:Given xml:lang="en">A</vcard:Given> <vcard:Family xml:lang="en">Huxley</vcard:Family> </rdf:Description> </vcard:N> </j.0:Person> </rdf:li> </rdf:Seq> </dc:creator> </rdf:Description> </j.0:JournalArticle> <j.0:Pubmed_id xml:lang="en">12991237</j.0:Pubmed_id> </rdf:Description> </j.0:reference> <cmeta:bio_entity xml:lang="en">Neuron</cmeta:bio_entity> <cmeta:species xml:lang="en">Squid</cmeta:species> <j.2:simulation> <rdf:Description rdf:about="rdf:#$Tpnot2"> <j.2:boundIntervals> <rdf:Description rdf:about="rdf:#$Upnot2"> <rdf:rest rdf:resource="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/> <rdf:first> <rdf:Description rdf:about="rdf:#$Vpnot2"> <j.2:nonstandard-pointDensity xml:lang="en">50000</j.2:nonstandard-pointDensity> <j.2:endingValue xml:lang="en">30</j.2:endingValue> <j.2:maximumStepSize xml:lang="en">0.1</j.2:maximumStepSize> </rdf:Description> </rdf:first> </rdf:Description> </j.2:boundIntervals> </rdf:Description> </j.2:simulation> <cmeta:comment> <rdf:Description rdf:about="rdf:#66bca445-cdee-4030-81ee-ed5b822bf666"> <rdf:value xml:lang="en">This is the CellML description of Hodgkin and Huxley's inspirational work on a mathematical description of currents through the membrane of a nerve fibre (axon) in a giant squid, and their application to the modelling of excitation in the nerve. It is generally regarded as the first example of a mathematical model of biology.</rdf:value> <dc:creator> <rdf:Description rdf:about="rdf:#6d8cd909-915e-4a88-96ee-33dcda056c46"> <vcard:FN xml:lang="en">Warren Hedley</vcard:FN> </rdf:Description> </dc:creator> </rdf:Description> </cmeta:comment> <dc:title xml:lang="en">The Classic Hodgkin-Huxley 1952 Model of A Squid Axon.</dc:title> <j.0:Pubmed_id xml:lang="en">12991237</j.0:Pubmed_id> </rdf:Description> </rdf:RDF>
C:\Users\chthompson\Dropbox\Work Related\Annotated Models\Hodgkin_1952\hodgkin_huxley_1952.cellml
Christopher Thompson
hodgkin_huxley_squid_axon_1952
Charge flow rate
Charge amount
sodium(1+)
potassium(1+)
calcium ion
Nerve fiber
Plasma membrane
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
Leak current across plasma membrane
Charge flow across the plasma membrane
Potassium current across plasma membrane
Sodium current across plasma membrane
Time Domain
Ionic leakage equilibrium potential
Maximum plasma membrane rest potential
Displacement of the membrane potential from its resting value
Ionic leak conductance of the plasma membrane
Leakage current across the plasma membrane
<apply> <eq /> <ci>E_L</ci> <apply> <plus /> <ci>E_R</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10.613</cn> </apply> </apply> <apply> <eq /> <ci>i_L</ci> <apply> <times /> <ci>g_L</ci> <apply> <minus /> <ci>V</ci> <ci>E_L</ci> </apply> </apply> </apply>
Plasma membrane charge capacity
Potassium current across the plasma membrane
Sodium current across the plasma membrane
Experimental charge stimulus.
<apply> <eq /> <ci>i_Stim</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="microA_per_cm2">20</cn> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millisecond">10</cn> </apply> <apply> <leq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millisecond">10.5</cn> </apply> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="microA_per_cm2">0</cn> </otherwise> </piecewise> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>V</ci> </apply> <apply> <divide /> <apply> <minus /> <apply> <plus /> <apply> <minus /> <ci>i_Stim</ci> </apply> <ci>i_Na</ci> <ci>i_K</ci> <ci>i_L</ci> </apply> </apply> <ci>Cm</ci> </apply> </apply>
Potassium ion equilibrium potential
Potassium conductance of the cell membrane
Proportion of activating molecules inside of cell
<apply> <eq /> <ci>E_K</ci> <apply> <minus /> <ci>E_R</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">12</cn> </apply> </apply> <apply> <eq /> <ci>i_K</ci> <apply> <times /> <ci>g_K</ci> <apply> <power /> <ci>n</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn> </apply> <apply> <minus /> <ci>V</ci> <ci>E_K</ci> </apply> </apply> </apply>
N gate potassium ion transfer constant (out to in)
N gate potassium ion transfer constant (in to out)
<apply> <eq /> <ci>alpha_n</ci> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.01</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">65</cn> </apply> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">65</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <eq /> <ci>beta_n</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.125</cn> <apply> <exp /> <apply> <divide /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">80</cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>n</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_n</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>n</ci> </apply> </apply> <apply> <times /> <ci>beta_n</ci> <ci>n</ci> </apply> </apply> </apply>
Sodium ion equilibrium potential
Sodium conductance of the plasma membrane
Proportion of activating molecules inside cell
Proportion of inactivating molecules inside of cell
<apply> <eq /> <ci>E_Na</ci> <apply> <plus /> <ci>E_R</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">115</cn> </apply> </apply> <apply> <eq /> <ci>i_Na</ci> <apply> <times /> <ci>g_Na</ci> <apply> <power /> <ci>m</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> <ci>h</ci> <apply> <minus /> <ci>V</ci> <ci>E_Na</ci> </apply> </apply> </apply>
H gate sodium ion transfer constant (out to in)
H gate sodium ion transfer constant (in to out)
<apply> <eq /> <ci>alpha_h</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">0.07</cn> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">20</cn> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>beta_h</ci> <apply> <divide /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">1</cn> <apply> <plus /> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">45</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>h</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_h</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>h</ci> </apply> </apply> <apply> <times /> <ci>beta_h</ci> <ci>h</ci> </apply> </apply> </apply>
M gate sodium ion transfer constant (out to in)
M gate sodium ion transfer constant (in to out)
<apply> <eq /> <ci>alpha_m</ci> <apply> <divide /> <apply> <times /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millivolt_millisecond">0.1</cn> </apply> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <apply> <minus /> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">50</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">10</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <eq /> <ci>beta_m</ci> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_millisecond">4</cn> <apply> <exp /> <apply> <divide /> <apply> <minus /> <apply> <plus /> <ci>V</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">75</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="millivolt">18</cn> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>m</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_m</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>m</ci> </apply> </apply> <apply> <times /> <ci>beta_m</ci> <ci>m</ci> </apply> </apply> </apply>